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3 years ago

7

1) A population of genetically modified

1 answer:

TiliK225 [7]3 years ago

7 0

This is a linear equation or y=mx+c. Where y is the number of mosquitos at a particular month and x is the number of months. We know the initial population of the mosquitoes is c=20. They population doubles every month so this is the gradient, m=2. Therefore the equation for the growth of the mosquito population is:
y = 2x + 20.

So after x= 10 months the mosquito population will be,
y=2(10)+20= 40.

There will be 40 mosquitoes after ten months.

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. A right cylindrical drum is to hold 7.35 cubic feet of liquid. Find the dimensions (radius of the base and height) of the drum

Drupady [299]

Answer:

$r=1.05\ \text{ft}$

$h=2.12\ \text{ft}$

$20.91\ \text{ft}^3$

Step-by-step explanation:

r = Radius

h = Height

Volume of cylinder = $7.35\ \text{ft}^3$

$V=\pi r^2h\\\Rightarrow h=\dfrac{V}{\pi r^2}\\\Rightarrow h=\dfrac{7.35}{\pi r^2}$

Surface area is given by

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi r^2+2\pi r\dfrac{7.35}{\pi r^2}\\\Rightarrow A=2\pi r^2+\dfrac{14.7}{r}$

Differentiating with respect to radius we get

$\dfrac{dA}{dr}=4\pi r-\dfrac{14.7}{r^2}$

Equating with zero we get

$0=4\pi r-\dfrac{14.7}{r^2}\\\Rightarrow 4\pi r=\dfrac{14.7}{r^2}\\\Rightarrow r^3=\dfrac{14.7}{4\pi}\\\Rightarrow r=(\dfrac{14.7}{4\pi})^{\dfrac{1}{3}}\\\Rightarrow r=1.05$

$\dfrac{d^2A}{dr^2}=4\pi-2\times \dfrac{14.7}{r^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=4\pi+2\times \dfrac{14.7}{1.05^3}\\\Rightarrow \dfrac{d^2A}{dr^2}=37.96>0$

So, the value of the function is minimum at $r=1.05$

$h=\dfrac{7.35}{\pi r^2}=\dfrac{7.35}{\pi 1.05^2}\\\Rightarrow h=2.12$

So, the radius and height which would minimize the surface area is 1.05 feet and 2.12 feet respectively.

Surface area

$A=2\pi r^2+2\pi rh\\\Rightarrow A=2\pi \times 1.05^2+2\pi 1.05\times 2.12\\\Rightarrow A=20.91\ \text{ft}^3$

The minimum surface area is $20.91\ \text{ft}^3$ .

8 0

3 years ago

Find the area of efg

butalik [34]

The area of EFG is 12 ft

6 0

3 years ago

Lemon drops and jelly beans are mixed to make a 100 pound mix. if the lemon drops cost $1.90 per pound and jelly beans cost $1.2

vladimir1956 [14]

L = lemon drops

J = jelly beans

L +J = 100

L=100-J

1.90L + 1.20J=1.48*100

1.90(100-j) +1.20J =148

190-1.90J+1.20J=148

190-0.7J=148

-0.7J=-42

J = 60

L=100-60 = 40

40 pounds of Lemon Drops are needed

4 0

3 years ago

hi I was just a little bit of time with my module and I didn't know what is answer of the module now please please be sure of th

GREYUIT [131]

1. 5 x 4 = A. 20

2.

$\frac{2}{5} \times 25 = 2 \times 5 = 10$

the answer is D. 25

3.

$\frac{3}{5} \div 15 = \frac{3}{5} \times \frac{1}{15} = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}$

the answer is A. 1/25

4.

$4 \div \frac{1}{2} = 4 \times \frac{2}{1} = 8$

the answer is C. 8

5.

$9 \div \frac{1}{3} = 9 \times \frac{3}{1} = 27$

the answer is D. 27

6.

$20 \div \frac{1}{4} = 20 \times \frac{4}{1} = 80$

the answer is D. 80

7.

$\frac{9}{10} \div \frac{1}{2} = \frac{9}{10} \times \frac{2}{1} = \frac{18}{10} = \frac{9}{5} = 1 \frac{4}{5}$

the answer is C. 1 4/5

8.

$9 \div \frac{3}{2} = 9 \times \frac{2}{3} = \frac{18}{ 3} = 6$

the answer is B. 6

9.

$\frac{3}{4} \div \frac{3}{8} = \frac{3}{4} \times \frac{8}{3} = 2$

the answer is A. 2

3 0

3 years ago

Grace [21]

Answer and workings are in the attachments below.

8 0

3 years ago